Elliptic curve isogeny class 8.1-b over number field \(\Q(\sqrt{217}) \)

• Base field: \(\Q(\sqrt{217}) \)
• Label: 2.2.217.1-8.1-b
• Conductor: 8.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{217}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 54 \); class number \(1\).

Elliptic curves in class 8.1-b over \(\Q(\sqrt{217}) \)

Isogeny class 8.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
8.1-b1	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 1869574935893 a - 14705066746888\) , \( 3779122287683704783 a - 29724534929365231599\bigr] \)
8.1-b2	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -24740869992 a + 194598321582\) , \( 22630333034170967 a - 177997977712882799\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph